Angle of Repose

Q. A body kept on a smooth inclined plane inclination 1 in x will remain stationary relative to the inclined plane if the plane is given a horizontal acceleration equal to:

Q. A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical .A small block is kept in the bowl at a position where the radius makes an angle θ with vertical .The block rotates with the bowl without any slipping .The friction coefficient between block and bwl surface is μ Find the range of the angular speed for whichblock will not slip

Q. A hollow sphere f mass m and radius R is rolling without slipping on a rough inclined plane having angle of inclination 45 degree.The value ofcoefficient of friction between the sphere& inclined plane is

Q.

A box is placed on an inclined plane and has to be pushed down. The angle of inclination is

1. Equal to angle of friction

2. More than angle of friction

3. Equal to angle of repose

4. Less than angle of repose

Q.

The value of contact angle for kerosene with solid surface.

1. 0⁰

2. 90⁰

3. 45⁰

4. 33⁰

Q. 33. In the arrangement shown all surfaces are frictionless. The rod R is constrained to move vertically. The vertical acceleration of R is a1 and the horizontal acceleration of the wedge is a2 . The ratio a 1 upon a2 is equal to

Q. Four identical blocks of length L are arranged one over other , the maximum dis†an ce of uppemost block from the edge of lower most block is x such that no block tumbles Then x is

Q. 93. Two balls are projected with same speed u at angles alpha n beta with horizontal. Their path shown in figure. Ratio of their time of flight is

Q. 11.A DISC IN WHICH SEVERAL GROOVES ARE CUT ALONG THE CHORD DRAWN FROM A POINT A, IS ARRANGED IN A VERTICLE PLANE , SEVERAL PARTICLES START SLIPPING FROM A ALONG GROOVES SIMULTANEOUSLY . ASSUMING FRICTION AND RESISTANCE NEGLIGIBLE , THE TIME TAKEN IN REACHING EDGE OF DISC WILL BE 1.MAXIMUM IN GROOVE AB 2.MAXIMUM IN GROOVE AD 3.SAME IN ALL GROOVES 4.ACCORDING TO HEIGHT OF B, C, D, E, F

Q. A solid cylindrical disc rolls sown on inclined plane having inclination 60^° with horizontal without slipping. The initial accelaration of the topmost point of the disc i

Q. An object takes time t1 to reach the bottom, when it is placed on the surface of a smooth inclined plane of inclination theta. If same object takes time t2 to reach the bottom, when it is allowe to slide down a rough inclined plane of same inclination theta (u=coefficient of friction between object and inclined plane). The ratio of t1/t2 i

Q. A ball is released from top of the smooth vertical tube .The angle made by the ball with vertical when it just leaves the contact from the inner surface of the tube

Q. A body is placed on an inclined plane. The coefficient of friction between the body and the plane is $\mu$. The plane is gradually tilted up. If $\theta$ is the inclination of the plane, then frictional force on the body is

1. constant upto $\theta ={\tan }^{-1}\left(\mu \right)$ and decrease after that
2. increases upto $\theta ={\tan }^{-1}\left(\mu \right)$and decrease after that
3. decreases upto $\theta ={\tan }^{-1}\left(\mu \right)$ and constant after that
4. Increases upto $\theta ={\tan }^{-1}\left(\mu \right)$ and constant after that

Q. 56.A motor boat travels across a river from a point A to point B on the opposite bank along the line AB making an angle alpha with the direction of flow of the river. The flag on the mast of the motor boat makes an angle beta with direction of motion. Find the speed of motor boat with respect to ground. Assuming velocity of wind is u perpendicular to the stream.

Q. 86. A body placed on an inclined plane just start sliding downwards when the plane is at inclined at an angle of 30^° to the horizontal. Find the acceleration of the body when it is inclined at an angle of 45^° with the horizontal.

Q. A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${30}^{\circ }$, the box starts to slip and slides $4.0\text{m}$ down the plank in $4.0\text{s}$. The coeffficient of static and kinetic friction between the box and the plank will respectively be

1. $0.4$ and $0.3$
2. $0.6$ and $0.6$
3. $0.6$ and $0.5$
4. $0.5$ and $0.6$

Q. A hollow cylinder is released from rest from the top of fixed incline of inclination θ and length l. If cylinder rolls without slipping, then speed of cylinder at bottom of incline is

Q. $$\begin{gathered} 30.Anobjecttakestime{t}_{1}toreachthebottom,whenitisplacedonthesurfaceofasmoothinclinedplaneofinclination\theta .Ifsameobjecttakestime{t}_{2}toreachthebottom,whenitisallowedtoslidedownaroughinclinedplaneofinclination\theta (\mu =coefficientoffrictionbetweenobjectandinclinedplane).theratioof\frac{t_1}{t_2} \\ 1.\sqrt{\frac{\sin \theta +\mu \cos \theta }{\cos \theta }} \\ 2.\sqrt{\frac{\sin \theta -\mu \cos \theta }{\cos \theta }} \\ 3.\sqrt{\frac{\sin \theta -\mu \cos \theta }{\sin \theta }} \\ 4.\sqrt{\frac{\sin \theta +\mu \cos \theta }{\sin \theta }} \end{gathered}$$

Q. 69. A Block is kept on a frictionless inclined surfacewith angle of incilnation alpha.The incline is given an acc. a to keep the block stationary. Then a is =

Q. 7.The figure shows a frictionless horizontal track which smoothly turns into a frictionless inclined surface of inclination θ. Aring of radius R rolling without slipping on the horizontal surface with angular speed, moves towards the inclined surface. The maximum distance along the incline plane moved by the ring is

Q. A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle theta. Coefficient of friction between the cylinder and the plane is u. For what maximum inclination theta will the cylinder roll without slipping?

Q. 23. A small block is released from point A in the figure it slides on the smooth surface and lease contact with the surface at b horizontally the horizontal range of the block will be maximum when H/h=

Q. is decrease in value of g due to latitude linear or paraboli

Q.

body just begins to slide down. The coefficient of friction is 1/√3. What is the angle of inclination?

1. 30⁰

2. 45⁰

3. 15⁰

4. 60⁰

Q. A block of mass $2\text{kg}$ rests on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7$. The frictional force on the block is

1. $9.8\text{N}$
2. $9.8\sqrt{3}\text{N}$
3. $4.9\sqrt{3}\text{N}$
4. $19.6\text{N}$

Q. A cylinder of radius R and mass M rolls without slipping down an inclined plane at an angle theta .coefficient of friction is mew.maximum angle of inclination cylinder roll without slipping is

Q. A turn of radius 20 m is banked for the vehicles going at a speed of 36 $km{h}^{-1}$. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speed of a vehicle so that it neither slips down nor skids up?

Q. 10.When an arrow is released from the bow then the end behind is the nearest to the ground, then why doesnt the arrow fall erect on the ground

Q.

34.A body slides down a rough inclined plane of angle of inclination 30degrees and takes time twice as great as the time taken in slipping down an identical frictionless plane.The coeffeicient of friction between the body and the plane is

Q. 28, A hollow sphere rolls down a rough inclined planewhose angle of inclination is θ, with horizontal. Forthe hollow sphere to undergo pure rolling, withoutslipping, the condition is \lbrack u coefficient of frictionbetween the hollow sphere and inclined plane\rbrack(1) tanθ < (2.5 μ) (2) tane> (2.5 μ)tane (3.5 H)(4) tane> (3.5 u)